According to Ephemeralstability
Although the following argument is for finitely many dimensions, it can be extended to countable or even uncountable-dimensional vector spaces.
Consider a bag of holding of dimension n. It can contain a vector space A of dimension at most n. Suppose it can contain other bags of holding. Then take the power set of A (i.e. set of all subsets of A). This can be represented as a set of bags of holding all containing subsets of A. There must be 2^n dimensions to contain all these bags and therefore the dimension of the bag of holding would be greater than n which is a contradiction. Therefore the bag cannot contain other bags.
I just read the "Golems are fantasy robots" thread, and this caught my eye. I wanted to see if anyone else had something to add.
This is a proposal that some GMs may allow, maybe not, but it is an argument for why bags of holding should be allowed into each other.
If you are considering the bag of holding to be of dimension X, then you overlook one important fact. In bag A, you have a given area, X. Bag B, physically, can be assumed to have an external area, Z, which is <X, right? We then define the internal area of bag B to be Y. Since we are assuming that the two bags are of equal size and open in to a non
coplanar vector space, then the area defined by X after you put bag B into bag A is not in fact X^2, but X-Z. It is the internal area of bag B that is important. Thus the total capacity of the two bags is X+Y-Z. However, if bags of holding are assumed open into coplanar spaces, then this entire argument is moot. However, you have an entirely new option open to you.
If bags of holding open into coplanar spaces, then no bag could be placed into another, safely. However, they all open into the same plane. A well provisioned party would be able to travel from bag to bag. Call this plane Bag-plane. Traveling on bag-plane could be hazardous, but what if you have a spell like intuit direction
? Then you can find your way from bag to bag, and eventually create a map of the bag-plane. This could be an entire world of adventures, as adventurers get the bright idea of either A: Looting other peoples' bags of holding, or B: building an easy access stronghold on the bag-plane, with portals
leading to and from bags placed on the Material Plane for very quick access anywhere, but without the telltale magical signature of a portal
Credits for this idea go to Kenzer and Co. Don't sue me, please.
Okay, I realize that in most campaigns, a bag of holding has a finite amount of space in it, and I think that is perfectly fine. However, then, unless you come up with some reason otherwise (Hint: magical fields), there is no good reason why one bag of holding could not contain another.
And, yes, I realize that many terms and descriptions were D&D. I apologize, I just think they are the best way to describe what I am trying to say. You should be able to translate fairly easily.Edit: On rereading ephe's post, I see what she was saying, and why it could be valid. However, I still stand by my argument. No offense, ephe.